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Worksheet: Magnitude of a 2D Vector

Q1:

Given that v = ⟨ 0 . 6 , βˆ’ 0 . 8 ⟩ , find the value of | | v .

Q2:

What is the magnitude of the vector οƒ  𝐴 𝐡 , where 𝐴 = ( 5 , βˆ’ 9 ) and 𝐡 = ( 9 , 1 ) ?

  • A √ 1 0
  • B4
  • C116
  • D 2 √ 2 9
  • E √ 1 4

Q3:

The vector v is shown on the grid of unit squares below. Find the value of | | v .

Q4:

Find the magnitude of the vector v shown on the grid of unit squares below.

Q5:

What is the difference between scalar quantities and vector quantities?

  • AScalar quantities only have magnitude; vector quantities only have direction.
  • BScalar quantities have both magnitude and direction; vector quantities only have magnitude.
  • CScalar quantities only have direction; vector quantities only have magnitude.
  • DVector quantities have both magnitude and direction; scalar quantities only have magnitude.
  • EScalar quantities have both magnitude and direction; vector quantities only have direction.

Q6:

Displacement is a vector quantity which combines distance and direction. For example, the displacement of Washington, DC, from New York City is 200 miles southwest.

What is the magnitude of the displacement?

  • A 200 miles southwest
  • B200
  • Cmiles
  • D 200 miles
  • Emiles southwest

What is the direction of this displacement?

  • Asouthwest
  • B 200 miles southwest
  • CWashington, DC
  • DNew York City
  • Emiles southwest

Q7:

Find the magnitude of the vector v shown on the grid of unit squares below.

  • A7
  • B50
  • C βˆ’ 1
  • D 5 √ 2
  • E 2 √ 5

Q8:

Find the magnitude of the vector v shown on the grid of unit squares below.

Q9:

Consider the vectors u = ⟨ 2 , 3 ⟩ and v = ⟨ 4 , 6 ⟩ .

What is the magnitude of u ? Give your answer correct to two decimal places if needed.

What is the magnitude of v ? Give your answer correct to two decimal places if needed.

What is the magnitude of u v + ? Give your answer correct to two decimal places if needed.

Q10:

What is the magnitude of the vector ⟨ 0 , βˆ’ 7 ⟩ ?

Q11:

Given that v = ⟨ βˆ’ 3 , 0 ⟩ , find the value of | | v .

Q12:

The vector v is shown on the grid of unit squares below. Find the value of v .

  • A √ 3
  • B √ 2
  • C5
  • D √ 5
  • E9

Q13:

Which of the following is a direction vector for a line parallel to the -axis?

  • A
  • B

Q14:

Suppose the points 𝐴 and 𝐡 have coordinates ( π‘₯ , 𝑦 ) 1 1 and ( π‘₯ , 𝑦 ) 2 2 respectively. Find the magnitude of the vector οƒ  𝐴 𝐡 in terms of π‘₯ 1 , 𝑦 1 , π‘₯ 2 , and 𝑦 2 .

  • A  ( π‘₯ βˆ’ π‘₯ ) βˆ’ ( 𝑦 βˆ’ 𝑦 ) 2 1 2 2 1 2
  • B  ( π‘₯ βˆ’ π‘₯ ) 2 1 2
  • C √ π‘₯ βˆ’ π‘₯ 2 1
  • D  ( π‘₯ βˆ’ π‘₯ ) + ( 𝑦 βˆ’ 𝑦 ) 2 1 2 2 1 2
  • E √ 𝑦 βˆ’ 𝑦 2 1

Q15:

The vector v is shown on the grid of unit squares below. Find the value of | | v .

  • A √ 3
  • B βˆ’ 2
  • C13
  • D √ 1 3
  • E √ 5

Q16:

Water boils at 2 1 2 ∘ F . Is this temperature a scalar or vector quantity?

  • A scalar
  • B vector

The freezing point of water is 1 8 0 ∘ F lower than the boiling point of water. Is the freezing point of water a scalar or vector quantity?

  • A scalar
  • B vector

Q17:

An astronomer observes a comet through her telescope and notes down its location. Which additional piece of information would allow her to predict the position of the comet in an hour’s time?

  • Athe comet’s distance from her
  • Bthe comet’s speed
  • Cthe comet’s displacement relative to her
  • Dthe comet’s velocity

Q18:

Given that , find .

  • A4
  • B200
  • C
  • D

Q19:

Find the magnitude of the vector v shown on the grid of unit squares below.

Q20:

The vector v is shown on the grid of unit squares below. Find the value of | | v .

Q21:

Given that , where and are two perpendicular unit vectors, find .

  • A
  • B
  • C
  • D

Q22:

The vector v is shown on the grid of unit squares below. Find the value of | | v .

Q23:

What is the magnitude of the vector ⟨ 3 . 2 , 1 2 . 6 ⟩ ?

Q24:

Noah is 25 years old. Is his age a scalar or vector quantity?

  • A scalar
  • B vector

Noah’s father is 31 years older than him. Is his father’s age a scalar or vector quantity?

  • A scalar
  • B vector

Q25:

Find the magnitude of the vector v shown on the grid of unit squares below.